If \(p=\frac{2d}{d+2k}\)  and \(q=p^{\prime }=\frac{2d}{d-2k}\) , then (REF ) can be obtained from the Carleman inequality with weights \(|x|^{-\tau }\)  proved in [1]}, [2]}, as was observed by Wolff [3]} for the case \(k=1\) . See [4]}. In our forthcoming work [5]}, we consider the strong UCP for the polyharmonic operators and extend the previous results in [1]}, [7]}, [8]}, [2]}, [10]}.
